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arXiv · 2508.18228

Improved bounds for radial projections in the plane

Marianna Csornyei·D. M. Stull
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Abstract

We improve the best known lower bound for the dimension of radial projections of sets in the plane. We show that if $X,Y$ are Borel sets in $\R^2$, $X$ is not contained in any line and $\dim_H(X)>0$, then $$\sup\limits_{x\in X} \dim_H(\pi_x Y) \geq \min\left\{(\dim_H(Y) + \dim_H(X))/2, \dim_H(Y), 1\right\},$$ where $\pi_x Y$ is the radial projection of the set $Y$ from the point $x$.

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Marianna Csornyei, D. M. Stull. 2025-08-25. Improved bounds for radial projections in the plane. https://arxiv.org/abs/2508.18228

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